Simplify the following expression: $ z = \dfrac{4p + 5}{p - 8} + 3 $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the second expression by $\dfrac{p - 8}{p - 8}$ $ \dfrac{-3}{1} \times \dfrac{p - 8}{p - 8} = \dfrac{-3p + 24}{p - 8} $ Therefore $ z = \dfrac{4p + 5}{p - 8} - \dfrac{-3p + 24}{p - 8} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{4p + 5 - (-3p + 24) }{p - 8} $ Distribute the negative sign: $z = \dfrac{4p + 5 + 3p - 24}{p - 8}$ $z = \dfrac{7p - 19}{p - 8}$